The explosive growth of the Internet has created a demand for high data rates for business and residential users (SOHO—small office/house office). Because of the prevalence of twisted pair copper wires in existing telephone networks, much of the demand must be met by data communication protocols that are adapted to transmit data over these standard analog plain old telephone systems (POTS) lines. The need for high-speed access to the home and businesses appears to be ever increasing due in part to the availability of information, data, high-bandwidth video and the like from the world wide web. Because of this ever increasing demand, higher speed modems are required.
Originally data transmission over POTS lines was accomplished using voice/data modems. These devices modulate data just like voice signals. As a results their theoretical data transfer speed limit is insufficient to deliver broadband content. Current voice/data modems appear to have reached a maximum data transfer speed of up to 56.6K bits/second.
Due to the inadequacy of voice/data modems, the industry looked for new solutions to delivering high speed data access over existing twisted pair copper telephone lines. One result of these efforts was the emergence of digital subscriber line technology (DSL). DSL provides high speed data transmission over relative short distances of twisted pair lines by utilizing the portion of the available bandwidth in the twisted pair above the few thousand kilohertz utilized by voice communications. Because of bandwidth limitation (4 KHz), and power limitation of the telephone network, line coding schemes are used to encode digital signals into analog signals that convey the analog information over the analog telephone network. The line coding schemes manipulate the analog carrier signal, which has three attributes, amplitude, phase and frequency. One or more of such attributes may be manipulated by known modulation techniques such as, for example, quadrature amplitude modulation (QAM) whereby the carrier signal's phase and amplitude is modulated to encode more data within a frequency bandwidth. One example of a QAM modulation system sends two bits of information per QAM symbol, where the digital values can be encoded and the corresponding amplitude and phase can be represented using a constellation. Increasing the constellation size, that is number of points (bits), will cause the bit density per symbol to increase, and hence achieve higher data rates.
An upper limit on this process of constellation mapping stems from the fact that as the constellation size increases, the granularity of the phase and the amplitude difference between different constellation points diminishes, making it increasingly difficult to decode the constellation points, especially in the presence of noise. One way of circumventing this problem is to increase the Euclidean distance between symbols by employing trellis coding. Trellis coding is particularly well suited for this because it is bandwidth efficient, since the symbol rate and required bandwidth is not increased. As noted above, as the constellation size gets bigger, the problem of detecting a constellation increases due to the greater symbol density increases. Therefore, a way of counter-acting the effects the short Euclidean distance between symbols is to partition the quadrature amplitude modulated signal into subsets, thereby creating an acceptable Euclidean distance between symbols.
In a typical DSL system, data from a personal computer or other equipment at the customer premise (CPE) is sent to a transmitter which arranges the data into frame packets; the packetized signal is then quadrature amplitude modulation encoded and error encoded using trellis encoding to improve the noise immunity using a convolutional coder to select a sequence of subsets in a partitioned signal constellation. A numerical symbol vector is trellis encoded. The trellis encoding starts with the most significant symbol and ends with the least significant symbol of the vector, a process which employs convolutional encoding that converts the input symbol to another symbol and then maps the encoded symbol to its corresponding 16 QAM signal constellation point.
Trellis-coded modulation (TCM) is a well-established technique in digital communications. A turbo code combines binary component codes (which typically include trellis codes) with interleaving. A turbo code is primarily composed of parallel concatenated convolutional codes (PCCCs) implemented by two or more constituent systematic encoders joined through one or more interleavers. The input information bits are fed through a first encoder and, after having been scrambled by the interleaver, enter a second encoder. A code word of a parallel concatenated code consists of the input bits to the first encoder followed by a parity check bits of both encoders. The suboptimal iterative decoding structure for such a code is modular, and consists of a set of concatenated decoding modules—one for each constituent code—connected through an interleaver identical to the one in the encoder side. Each decoder performs weighted soft decoding of the input sequence. PCCCs yield very large coding gains at the cost of a reduction in the data rate and/or an increase in bandwidth. Convergence analysis of iterative decoding algorithms for turbo codes has received much attention recently due to its usefulness in predicting code performance, and its ability to provide insights into the encoder structure and help with the code design. Turbo trellis coded modulation (TTCM), conjoins Ungerboeck's signal space partition with turbo coding to achieve significant coding gains without increasing bandwidth. The performance of TTCM schemes depends on the Euclidean distances between sequences of symbols rather than the Hamming distance of the underlying binary codes, the structure of TTCM schemes is more complex and difficult to analyze. Hence the convergence analysis is even more important for TTCM in order to facilitate the design and comparison between schemes.
Because the Euclidean distance between symbols points is a paramount feature of the QAM signal, and since the discrete multi-tone modulation scheme employed by some of the high data rate systems such as DSL requires transmitting of at least three DMT symbols per tone, there is a need to use more efficient Trellis codes in DMT.